Computer of the slide rule type



*LEVKOVITSCH Oct. 29, 1946.

RVIGOUDIME COMPUTER OF THE SLIDE RULE TYPE Filed July 7, 1943 4Sheets-Sheet l AGAINST D AGAINST E SET ARM$ r0 A ANDB' SET INDEX TO A NCm VA E D W T E 5 READ VALUES OF I- AND I" AGAINST a READ vALuE 0F I I/EmPM W ,1

,1946. PQGOUDIME-LEVKOV1TSCH 1 COMPUTER OF THE SLIDE RULE TYPE FiledJuly 7, 1945 4 Sheets-Sheet 2 COURSE TRACK snArrowhTzAqlinst'fiJundAmdszi' pink! Agind'fsrud Band at oin'ltrTurnwriowAMNDMGLEmdDnlI-T 1946 P. GQUDIME-LEVKOVITSCH 2,410,210

COMPUTER OF THE SLI DE RULE TYPE 4 Sheets-Sheet 3 Filed July 7, 1945OTHIIEIGIHI 1946- P. GOUDlME-LEVKOVITSCH 2,410,210

COMPUTER OF ,THE SLIEDE RULE TYPE 4 Sheets-Sheet 4- Filed July 7, 1943usynz 9 was-M, 6%

Patented Oct. 29, 1946 COMPUTER OF THE SLIDE RULE TYPE PaulGoudime-Levkovitsch, Wentworth, England,

London, England assignor to Simmonds Aerocessories Limited,

Application July 7, 1943, Serial No. 493,774 In Great BritainJuly 29,1942 This invention relates to computers of the slide rule type and moreparticularly but not exclusively to computers adapted for solvingcertain problems which occur in air navigation.

The conventional way of solving on a slide rule an equation of the formwhere C and D represent variables is first to determine the value of C/Dand then to subtract the value found from 1 in order to find at.

In the improved computer according .to the present invention there iscombined with an ordinary logarithmic scale of numbers (hereinafterreferred to as the main scale), a relatively movable auxiliary scalewhereby the value may be read off directly. I

The main scale is plotted in accordance with the expression d'=K logy,where d is the linear distance from the origin or index of the scale ofany given graduation y, and K is a constant of proportionality. Theauxiliary scale is plotted in accordance with the expression 10" d logwhere d is the linear distance from the origin or index of the scale ofany given graduation y, n is a whole number, chosen according to thedecade over which 1/ is to be measured, such that the value of remainspositive at the maximumvalue of y, and K is the same constant ofproportionality as that used in plotting the main scale.

In the use of a computer having such an auxiliary scale, the index ofthe auxiliary scale is set against the value of C on the main scale andagainst the value of D on the main scale the value of :t'is read offdirectly on the auxiliary scale.

That such a pair of cooperating scales may be used to determine thevalue of directly may be shown in the following manner. With the indexof the auxiliary scale set against any graduation 1111' on the mainscale, if d1 be the distance from the index of the main scale to thegraduation yr, d2 be the distance from the index of the main scale toanother graduation ya on the main scale, where C and D representvariables, and .da be the distance from the index of the auxiliary scaleto the graduation 2 Claims. (Cl. 235 -84) ya on that scale which isopposite the graduation 11/2 on the main scale, then d3=d2'-d1'. Fromthe definition of the scales, d1=K log yr,

and substitution of these values in the equation d3=d2'd1' gives y3=10"(1- -r'-;,). Q In. the particular case under consideration, y1=C andy2'=D so that For convenience, the factor will be called'A and thefactor Oneconvenient form of computer for solving Equation 2 isillustrated inFigures l and 2 of 3 the accompanying drawings, Figure 1being a top plan view of the computer and Figure 2 a similar view of thecomputer with the upper disc removed.

The computer comprises two concentric, superposed, relatively rotatablediscs, the lower disc I having a greater diameter than the upper disc 2.On the lower disc and beneath the upper disc a circular main scale 3 isengraved and a portion of this scale is visible through an arcuateWindow in the upper disc. rived as shown above, is engraved around theinner edge of the window in the upper disc.

The first stage in solving the equation is to determine the values of Aand B. The upper disc 2 is rotated until the index of the auxiliaryscale 4 is set to the value of C on the main scale, and opposite thevalues of D and E on the main scale the values of A and B respectivelyare read off directly on the auxiliary scale. Dividing A by B will give2. For this purpose an additional logarithmic scale of numbers, 6,hereinafter called the "log A and B scale, is engraved around the edgeof the lower disc I and a further logarithmic scale of numbers, I,called the log 2 scale, is engraved around the edge of the upper disc 2.Two radially-extending arms 8, 9, called A" and B, respectively, arearranged to rotate about the axis of the discs and to be set against thelog A and B scale. This form of computer functions as follows:

The values of A and B having been determined, the movable arms A and Bare set to the values which have been found. The upper disc 2 is thenrotated so that the index of the g 2 scale 1 comes opposite the arm Aand then the value of z may be read off directly on the log 2 scaleagainst the arm B.

Figure 1 shows the computer set for solving the equation 145 Let) Theindex of the auxiliary scale 4 is set against the numeral 4 on the mainscale 3, the value of 1% being given on the auxiliary scale opposite 5on the main scale as 0.2, and the value of L1 6 being given opposite 10on the main scale as 0.6. From the values of A and B thus obtained, thevalue of z is readily determined in the manner given above.

According to an important feature of the present invention, a computerof the type above described is adapted to solve a problem which occursin air navigation when finding the wind speed and direction by what isknown as the four point bearing method.

The procedure involved consists in timing the aircraft between certainintervals during which bearings are taken of a fixed object.

The aircraft flies on any desired course and when vertically over aselected object an artificial smoke cloud is released from the aircraftand a stop watch is started. The pilot then turns 180 and flies on asteady course. After about 90 seconds he makes another 180 turn andflies on a reciprocal course. If the turns have been correctly made theaircraft will now be heading straight for the smoke cloud, which willhave drifted away from the object. The time of passing through the cloudis noted and is called T1. The aircraft continues to fly on the samecourse and when the object is seen to bear 90 the time T2 is taken;finally when the object bears 135 the time T3 is taken.

The auxiliary scale 4, de- I Figure 3 illustrates the theory of themethod when dealing with a headwind. When a tailwind is involved, theobject comes abeam before the aircraft enters the smoke cloud and thetime T1 will be greater than T2.

From the knowledge of the times, T1, T2, and T3, and of the airspeed ofthe aircraft, the wind angle, i. e. the angle between the aircraftscourse and the wind direction, the wind speed, the drift and thegroundspeed may be found. Dealing first with the wind angle 0, I havederived this as follows, reference being made to Figure 3, where:

O is the position of the object.

A, B and C are positions of the aircraft at times T1, T2 and T3respectively,

AH represents the course.

AC represents the track.

OA, DB and HC represent the direction of the wind.

0=wind angle.

=drift angle.

From Fig. 3 it will be seen that, if W is the wind velocity, V is theair speed and G is the ground speed, that and it can be shown that Z1 Wcos 6 V 1 and also that W (cos 0+sin 0) =V(1 V 3 Eliminating W, andsolving B, the equation becomes B -tan B (4) and Ta.

' One form of computer for solving the above problem is shown in Figures4 to 8 of the accombeing a cross sectional view taken online 88 ofFigure 4.

The computer comprises two concentric relatively rotatable discs 1,20,the lower disc having a greater diameter than the upper disc l0. On disc20 and beneath disc It the main scale 2| is engraved. This scale iscalled the time scale and corresponds to the times T1, T2, A portion ofthe time scale 2| is visible through an acrcuate window II in disc H).The

auxiliary scale I2, which is similar to scale 4 of the computer shown inFigures 1 and '2, is

engraved around the inner edge of window I in disc ID. A log A and Bscale 22 (similar to scale 6 of Figures 1 and 2) is engraved around theperiphery of disc 20.

A third concentric, relatively rotatable disc 3|) is mounted immediatelybeneath disc 20 and this disc bears a scale 3| of log tan 0 called thewind angle scale. An arm 32 (the A arm) is secured to disc 30 so as torotate therewith and reads against the log A and B scale 22, while afourth concentric, relatively rotatable disc 40, mounted beneath disc30, has an arm 4| (the B arm) which also reads against scale 22. Thedisc has an arcuate window 42 through which a portion of scale 3| isvisible.

In order to find the wind angle the index of the auxiliary scale I2 isset to the appropriate value of T2 0n the time scale 2|. Opposite T1 andT3 on the. time scale 2| the values of A and B respectively are read offon the auxiliary scale l2. The A and B arms 32, 4| are set to theirrespective values on the log A and B scale 22, and, on turning over thecomputer, the wind angle may be read off on its scale 3| against the Barm 4|.

A convenient way of finding the wind speed with this form of computer isto utilize the angle of drift This may be read off directly since tan=B. This can be shown by reference to Figure 3 where it is seen thatSince BD=W (T2T1) and OA=WT1 it follows that tan WT, cos 0 and thus thatL tan tan 0( 1) Substituting for tan 0 the value given in Equation 3, wehave Thus by marking off on the log A and B scale,

values of i such that 4 is equal to tan B the drift angle may be readoff directly against the arm B at the same time that the wind angle 0 isread off. In the computer shown in the drawings,

however, a separatedrift angle logarithmic scale '23 derived as alreadydescribed is engraved on the reverse side of the disc 20, and a portionof this scale-is visible through window 43- in arm 4|. The computershown in the drawings is set to show the values of the wind angle anddrift angle in the case of a headwind where:

Course through cloud 60 true Trueairspeed 150 knots Bearing of object Toport T1 l74gseconds T2 e 200 seconds T3 220 seconds From the front ofthe computer it is seen that the values of A and B respectively are 15and 9 and with the A and B arms set to these .values on the log A and Bscale 22, the wind angle 30 is read off on its scale against the B arm4| and the drift angle 5 against the said arm on the drift angle scale23.

As the object bears to port, the wind direction is 30 or 30 true, whilethe track is +5 or true.

- The wind speed W and groundspeed Gare found by a separate calculation.For example as shown in the drawings, there may be engraved on disc 40 acircular logarithmic airspeed scale 44, numbered say 5-400 M. P. H.,while on a fifth concentric, relatively rotatable disc 50 arrangedbeneath disc 40 there may be engraved a, circular logarithmic sine scale5| which reads against the airspeed scale 44. By the sine 35 formula twhere V denotes the airspeed. Hence it is only necessary to set theairspeed V, against the sum of the wind angle and drift angle (0+) andread off directly the wind speed W against the drift angle 5 and theground speed G against the wind angle 0.

In the example given above the sum of the wind angle and the drift is 35and it will be seen from the drawings that, on setting the airspeed 150against the angle 35, the groundspeed 130 knots is read off against thewind angle 30 and 50 the wind speed 23 knots is read off against thedrift angle 5.

As previously mentioned, in the case of a tailwind, T1 will be greaterthan T2. Thus T1 will appear against the right hand portion of scale 55I2, i. e. that part of the scale marked A and B in the drawings. In thecase of a tailwind, the wind angle scale 3| on disc 30 and the sinescale 5| on disc 50 are employed and means are preferably provided toremind the user that, for a 60 tailwind case, these scales are used. Forexample, the part of scale l2 marked A and B, and scales 3| and 5| maybe in red, as indicated in the drawings by these scales being doublelined, the other scales being in black.

The wind direction, the wind speed and the drift having been determinedin the manner described above, the computer may then be used for findingthe course to steer, the drift and the groundspeed for any new track.The angle which the wind makes with the proposed new track is determinedand is called the new wind angle+drift. Setting this value on the sinescale 5| on disc 50 against the airspeed on the airspeed scale 44 ondisc 40 enables the new drift to be read off on scale 5| against thewind speed on scale 44 and the new groundspeed to be read ofi on scale44 against the wind angle on scale The following example will make thisclear:

Airspeed 150 knots Wind direction as found true Wind speed as found 21knots New track to be made good 340 true The angle between the new trackand the wind direction is 360340+10, or 30, and this is called the newwind angle+drift.

1. Set new wind angle+drift of 30 on scale 51 against the airspeed of150 knots on scale 44.

2. Against the wind speed of 21 knots on scale 44 read off on scale 5|the drift on the new course of 4.

3. Against the wind angle 260 (30-4) on scale 5| read off on scale 44the groundspeed on the new course of 130 knots.

Hence the new course is 340+4=344 true.

I claim:

1. In a computer of the slide rule type for computing wind direction bythe four point bearing method, a member having a scale which is plottedin accordance with the expression d=K log y, where d is the lineardistance from the origin of the scale of any given graduation 3 and K isa constant of proportionality, and a second relatively movable memberhaving a scale which cooperates with the first-mentioned scale and whichis plotted in accordance with the expression 10" d K log where d is thelinear distance from the origin of the scale of any given graduation y,n is a whole number chosen according to the decade over which 11 is tobe measured, such that the value of 10" K M (T6113) remains positive atthe maximum value of y, and K is the same constant of proportionality asthat used in plotting the first-mentioned scale.

2. A computer of the slide rule type for solving an equation of the formwhere C and D represent variables, said computer comprising a memberhaving a scale which is plotted in accordance with the expression d'=Klog y, where d is the linear distance from the origin of the scale ofany given graduation y and K is a constant of proportionality, and asecond relatively movable member having a scale which cooperates withthe first-mentioned scale and which is plotted in accordance with theexpression d=IC 10g where d is the linear distance from the origin ofthe scale of any given graduation y, n is a whole number, chosenaccording to the decade over which 11 is to be measured, such that thevalue that used in plotting the first-mentioned scale.

PAUL GOUDIME-LEVKOVITSCH.

